3 ms·
Measure theory also tells you that if you managed to make two solid balls of radius 1 from cutting up a single solid ball of radius 1, then some of the intermed
by joppy 7y ago
Measure theory also tells you that if you managed to make two solid balls of radius 1 from cutting up a single solid ball of radius 1, then some of the intermediate pieces you cut the original ball into must have been non-measurable sets. Non-measurable sets are known to behave counterintuitively, and are avoided when using measure theory (since they cannot be assigned a volume).
Is “garbage in, garbage out” so unreasonable?
- aeneasmackenzie 7y agoWhy use a system where you have to check if you put garbage in?
- joppy 7y agoYou have to check if a number is zero before you divide by it, you need to check if a number is positive before you take its log, you need to check it a set is measurable before you measure it or integrate over it. I don’t really see how any of these are significantly different.